A machine tool removes workpiece material by cutting, grinding, lathe turning, polishing, or electric discharge machining. The modern machine tool is provided with a computerized numerical controller (“CNC”) and a motion controller. The CNC interprets a numeric control program (“NC program”) and generates position data, velocity data and data indicative of the other state values. The CNC is equipped with an operation panel and a display device as a human interface, and has various functions which enable an operator to run a machine tool. The motion controller controls a servomotor so as to drive a movable member in a desired direction at a desired velocity and stop it at a desired position. The motion controller receives position data and velocity data from the CNC and calculates acceleration, compensation such as pitch error compensation, feedforward control, feedback control and determines a tool path which it supplies as a control signal to the servomotor.
Attempts to apply a sliding mode control to the servo system for machine tools have been made, and improved positioning accuracy is expected. Recently, a linear motor driven machine tool has become common. As it has no transmission for transmitting a drive force of a rotary servomotor to a movable member, backlash is eliminated. Therefore, the sliding mode control method particularly suits the linear motor driven machine tool and good performance results which offset the increased design cost are expected.
The sliding mode control is applicable to a discontinuously changing nonlinear system, a variable parameter system and a system having uncertain disturbances. In general, a sliding mode controller is constructed as a variable structure, proportional-integral controller. The sliding mode controller ensures robustness against modeling errors and uncertain disturbances by the switching of the control input which is provided to the controlled system. In the sliding mode controller, the control input is usually divided into a linear control input and a nonlinear control input. The linear control input keeps the state of the controlled system on a switching hyperplane while the nonlinear control input forces the state of the controlled system to remain on the switching hyperplane in the presence of modeling errors and uncertain disturbances. The designer of the sliding mode controller must set the switching gain a priori according to the expected maximum of the uncertain disturbance so that the disturbance can be canceled by the nonlinear control input. If the switching gain is set to an unduly small value, the state of the controlled system may not be maintained on a switching hyperplane. Additionally, an excessively large switching gain is likely to result in undesirable “chattering” behavior.
Therefore, there is a need to provide a motion controller with a sliding mode controller in which the state of the controlled system can be maintained on the switching hyperplane regardless of the magnitude of the disturbance.